From JFK, you can fly UA ps service to SFO or LAX. You can then connect to LIH or OGG (LIH will be domestic 757s, OGG will be 777 or 767 or 757 (SFO-OGG), or 767/757 (LAX)). Or JFK-ORD-OGG (777; the non-stop is only on weekends these days).
@:-)An alternative is to fly on CO EWR to HNL non-stop, and then connect via a local airline to Maui or Kauai. That is a 767 with business/first seating up front. You can use your UA miles for this as well.
All the UA flights to HI have baby changing tables in some of the restrooms.